MathDB
| BD | + | AM | + | AN | = | CD | + | AP | + | AQ |, equilateral and circle

Source: Switzerland - Swiss MO 2006 p2

July 18, 2020
geometryEquilateralcircle

Problem Statement

Let ABCABC be an equilateral triangle and let DD be an inner point of the side BCBC. A circle is tangent to BCBC at DD and intersects the sides ABAB and ACAC in the inner points M,NM, N and P,QP, Q respectively. Prove that ∣BD∣+∣AM∣+∣AN∣=∣CD∣+∣AP∣+∣AQ∣|BD| + |AM| + |AN| = |CD| + |AP| + |AQ|.
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